In my opinion, you should just forget about the girl and work on your technique. Seriously, sitting silent after a girl whines about her looks and then doesn't give you her number? That's just so full of date openings I positively cry over the fact that you just sat there saying nothing.
What could you have said? Well, any of the following:
"So you complain that guys don't ask you your number, but you don't want to give it out anyway?"
"You know, I am a guy, and I am asking for your number. Did you intend to say "no" to everyone who asks, or just me?"
"So... ...did you want for people to ask you for your number, or did you want people to actually call you for a date? It would help if you actually gave it out, you know."
"So I can't have your number now. Do you suppose I can convince you to give it to me tomorrow, over lunch maybe?"
"Um, do you actually have a number to give, or are you just bluffing?"
"Ooooh! That was way harsh, woman! You could at least have given me the number of some pizza place or chinese takeout. Preferrably good chinese takeout places."
Whether extremely good or extremely bad, your goal is to make a lasting impression. It's far easier to turn a woman to your favor when she thinks you're the Antichrist than when she doesn't even remember your face.